This version of the preface to the special issue of the Journal of Engineering Mathematics on “Practical methods and rigorous theories in numerical algebra and scientific computing” was retracted by the Editors-in-Chief with the agreement of the authors because it was based too closely on a preface the authors had co-written for a previous special issue of another journal [Bai, Duff and Reichel, Numer. Linear Algebra Appl. 2012 19, 893–895, doi:10.1002/nla.1857].